第四次积分训练赛

A 

Ball

Description

给a个黑球和b个白球，这些球除了颜色外没有别的不同，现随机的摸c个球，问至少有一个黑球的概率是多少？

Input

第一行,一个整数T表示测试组数( 0 < T \leq 1000<T≤100).
接下来T行，每行有三个用空格隔开的整数a,b,ca,b,c . (0 < a + b < 1e9, 0 < c <= b0<a+b<1e9,0<c<=b)

Output

对每个测试数据，请在一行中输出一个整数表示答案.(答案是一个p/q的形式且是模MOD下的意义，所以对于p/q就是 p * inv（q）. MOD = 1e9 + 7MOD=1e9+7)

Sample Input 1 

1

3 2 1

Sample Output 1

200000002

Source

lzs

思路：

1 - C(b,c) / C(a + b,c)求q的逆元，用费马小定理

但要注意一点就是a + b的数据量在1e9，暴力求a + b的阶乘肯定是不可能的，我们只能靠线下打表才能过，线下打表大致就是分块把时间复杂度从1e9缩到最大为块的大小

#include<bits/stdc++.h>
#define ll long long
using namespace std;/*  */
const ll mod = (int)1e9 + 7;
const int maxn = (int)1e4 + 50;
const int MAXN = (int)1e5;
//打表结果
ll f[maxn] = {1,457992974,107146451,373281933,559805077,154425679,679209364,526226141,644158465,730342129,641102369,99410016,363599536,361684231,539157852,448516387,309854856,95657988,663484182,311407840,578095319,229611066,765808214,142477924,585806050,119948046,579773866,816761238,861745250,639926530,5832229,630915411,242744764,932799119,899032987,929795683,150478174,609593566,627860803,358784546,259081142,57134788,544918953,8837465,907400235,59433257,421968194,500425006,278955367,248057675,974067448,293296655,996965954,212873022,473966292,261465122,479920311,214054614,752161465,719792849,316220877,224748329,1575312,652382508,620898940,663134272,405577532,116225742,956413299,257438891,690120224,437383740,24521750,596209708,576078970,304661605,929871923,412584039,14422365,604303898,251368199,808427728,582439362,55596303,220087090,704262886,98361446,295620142,763414075,927340096,980250487,248981102,618104354,839684660,398723029,386267146,764421236,558837848,476998749,345911460,682498929,58865407,152611299,37365474,345470378,681184885,403024660,947000742,140864216,22803916,134623568,733842728,373126171,337899910,461157687,427907847,363224613,642502601,526497651,759652538,95936601,173914411,19447777,382610562,584319463,140928835,569582206,226022701,9045328,784835785,933097914,76048860,959173997,780658683,559096347,391177708,12442609,40743573,508362944,781264818,167332441,33592533,75538458,714210512,275742306,739650465,137855279,889166166,60332461,798657991,598816162,464484063,31223863,344176836,767213175,292015879,564190300,296547306,222078457,977909564,336060741,474159159,632048012,952625711,895642779,810640932,171183381,305391286,851161246,209567103,248744620,551739578,635103992,526685249,605016577,892704918,853414712,566161015,546047842,894851390,626497524,433082692,867430659,512332467,904851726,118508240,475501650,815664143,298693437,652967545,288843364,865229790,52298443,803384326,743602491,406755567,479708090,643624459,125625755,316969704,491101308,708750650,662967999,571611259,385457627,668723114,482257159,899820643,393222011,401679067,245341950,587770205,474567292,725000295,196002818,560364972,754437203,498728445,542706821,970854495,565768255,246407879,524308015,724201825,545648343,913230882,58680787,702934318,792180189,131514392,246899319,192185054,99934426,98200674,788944266,756627904,676012445,734897886,610686655,130907341,968999,379198792,595032530,642903797,244819707,7998896,511710008,696896528,902492598,3525929,586350670,296000745,979137619,86414019,980655027,328019447,474700377,306429182,30153596,966484628,638587686,610696318,420932107,477267870,353049206,497857012,281562548,500956856,921459833,157600969,881746146,924389072,850268753,87892573,711117420,526658674,919203761,262557378,831442297,122316469,19426633,190298375,910061172,214146479,862345480,560607302,293462255,370787091,542955556,768910131,850500036,31318378,181909169,500033013,496532173,916364742,582702682,778006566,168757859,361307467,76479948,219226870,477639087,126712923,930180103,732041432,941723214,130794194,28581913,85186984,268124147,88516556,685075984,488636005,53790970,30473806,672818243,906976408,581968000,78103048,842267748,348586163,947532066,464777188,451116854,878381584,333707614,448457825,650009312,53500714,886294336,648763344,868829344,570443478,613566917,73995168,695702195,776902855,853242582,107560517,485348706,31109298,229827108,590398688,827117592,771153434,492711911,111567856,296974594,269232911,463847391,546178363,649090736,276477167,204857297,72518508,760019200,656049509,942731826,505080571,544075857,422316785,185735387,876081033,550588097,264638935,632593345,941126423,706629399,642498983,898187927,769005417,854821744,205765722,297803207,468116664,596729075,409898960,466541843,190009221,798967520,644759890,743420839,206187615,198998756,359622660,526623452,836550874,952046139,202071291,82926604,130808582,924044367,848688381,23777891,59761470,924258126,204012302,450837733,960862718,723816384,547639586,535478979,87226689,53975412,320608814,517436639,173809161,63932312,478679185,156530778,571781438,807928028,681452055,305569485,278224088,545662462,710807771,29493652,581977264,721996174,820229375,49456224,979809664,480391065,222176885,526281212,927482461,151117811,44756165,299085602,643484121,522961673,277106101,374481484,814440466,489252071,587318335,589831644,15753781,323604647,21771073,153393495,433729686,268164416,359932651,48301315,364347439,90383486,945599636,172827403,695951947,800588969,106892865,757146415,213590923,169338716,599312274,192601723,455503344,398699886,668865790,675113999,708394300,139831846,983975503,135840345,334346960,475501867,167226923,530389102,852493922,499294891,922898261,415376,619965361,114785958,146628257,576550918,635060378,294587621,55789549,714006296,103228118,457685563,221896631,875018827,971180026,254653019,274155554,813805606,9027036,172340144,518728060,498342367,676243000,258170000,496205651,43217172,714008239,67347853,912590546,909565792,54071151,16783532,557470122,495844744,95325827,402811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02,790523771,794859549,916291845,318580210,60217575,874580373,668677123,65591903,513047302,910026008,178909003,613496200,881482632,916304134,747296925,42587322,548026212,957757479,437155518,812279408,918951065,792299597,899946391,321697039,36670825,857922528,43744543,84428155,957469762,79147005,929269243,270142104,321900901,944491355,775543604,427709220,528255018,674721611,381350331,629894526,169838765,889482960,512634493,817479361,262044551,445396258,339271869,970053019,186968777,870125056,687740343,320428001,303338827,901511835,924265341,9058966,327625657,860842034,789825490,851258730,296589615,904066718,121000338,520374634,217147361,653145383,171989322,87654126,867046994,457294725,490484575,988922932,967284733,599140106,644960213,679659893,838526218,580938783,63126637,694075816,819577801,603739686,492741665,543574940,812501999,971085075,510950308,671517513,370290353,18797131,916660987,216549068,152233223,858814345,343799473,477335006,246311854,335102896,271361010,164992964,852694071,554291156,165393390,338262892,21985433,8195350,302780015,160150497,483975089,361084936,682610501,509406823,680128316,803513526,114644779,573964644,321935156,685723887,473979326,677822059,53102426,163052139,917041303,617666448,95249276,954826526,207172258,782192657,877643222,623151847,492897596,527572212,532702135,829422649,745391035,768941501,478657069,56081734,429707160,841072969,344857140,198803488,741626808,19820900,779734593,309906471,877891340,642939667,305583444,224546239,53635336,744645153,496442755,960584207,348421260,787464577,116164597,867195255,73903881,197001309,226879956,562908177,536841269,363551706,709515651,368324673,30514807,412622873,630057303,389088357,875410153,792914276,131384366,99359978,386541987,653102924,307321014,994065976,953786104,730583919,627500870,292151509,377329025,573443769,613973085,816691591,599685896,974508445,708543683,966533706,845486631,333457751,301196854,264848873,894553004,759137421,309986645,574480664,371930700,364502974,416322416,775556523,859917803,281761694,767790141,879674443,389995666,20211256,766570439,325014894,379943099,957347508,676511002,792894374,888140011,755146193,824619763,437157360,802932692,946198358,619700091,625494526,373451745,948994836,487012980,596952378,639054294,83118246,752243809,52836141,756614559,114955307,847645126,710424773,925139828,886787632,23001875,268761837,557583419,234337026,860551136,894939441,823495900,818476649,95460945,987535081,578471809,459628134,12029751,348246100,676216445,751971766,576368335,520389069,78835193,52979524,960033065,494290402,120815665,610541980,961431677,592296500,73146164,300019098,119895268,230976447,630786699,98016105,612866870,593422313,291993453,92077788,954958912,23895805,585347275,571536697,206526983,486828649,707764537,441442575,245423562,628018983,847549272,119263545,954421367,724553294,384826244,201882845,374116154,97348051,247001105,782816485,241289571,527174998,550507082,993282622,249360270,420567331,378750527,539300380,976517503,681566251,646654592,555103342,958797332,911520292,946033733,788599446,883122906,886354425,616017573,716431887,216046746,788872381,999340546,283129306,575014853,682599498,85104325,392505761,219092361,312720425,205951465,127398072,877002932,231120229,676290554,383521365,989326738,299086439,765080455,622618140,3258987,599755664,95568681,78742678,894658473,433576760,434360362,474857680,330810163,944598142,780882948,597789250,163787210,311490118,385914044,510148825,74434897,326957567,723091468,433350723,822439091,908200376,35784547,525561111,118654619,128900492,696559662,751235252,973737505,240437894,598245292,168759145,895487487,907890920,139066955,606924610,915276325,353658242,547380283,61705100,869544707,762816834,306032293,778368564,59434732,933768689,590393084,523894858,267469129,926316480,698611116};
ll quick(ll a,ll b)//快速幂 
{
	ll ans = 1;
	a = a % mod;
	while (b)
	{
		if (b & 1)
			ans = ans * a % mod;
		a = a * a % mod;
		b >>= 1;
	}
	return ans;
}
ll inv(ll x)//费马小定理求逆元 
{
	return quick(x,mod - 2);
}ll solve(ll a) //分块后的阶乘 
{
	ll p = a / MAXN;
	ll l = p * MAXN + 1;
	ll ans = f[p];
	for (int i = l;i <= a;i ++)
		ans = ans * i % mod;
	return ans;
}
/*-------线下打表--------*/ 
//void init()
//{
//	int pos = 0;
//	ll ans = 1;
//	for (int i = 2;i <= (int)1e9;i ++)
//	{
//		ans = ans * i % mod;
//		if (i % 100000 == 0)
//			f[pos ++] = ans;
//	}
//	for (int i = 0;i < pos;i ++)
//		printf("%lld,",f[i]);
//}
/*-------线下打表--------*/ 
int main()
{
	int t;
	ll a,b,c;
	scanf("%d",&t);
	while (t --)
	{
		scanf("%lld %lld %lld",&a,&b,&c);
		ll ans = (solve(a + b - c) % mod * (solve(b) % mod)) % mod
		          * inv(solve(a + b) % mod * (solve(b - c) % mod) % mod) % mod;
		ans = (1 - ans) + mod;
		printf("%lld\n",ans);
	}
	return 0;	
}

B

存图方式，dfs

#include <bits/stdc++.h>
using namespace std;

const int MAXN = (int)1e6 + 5;
typedef pair<int, int> pii;  //先建立pair类型
vector<pii> G[MAXN];        // 再用vector
int cnt = 0, n, k, x , y, c;
inline void dfs(int v, int fa, int cost) {
    cnt += cost > k ? 1 : 0;
    for(auto &i : G[v]) if(i.first != fa) dfs(i.first, v, cost + i.second);
}

int main() {
    scanf("%d%d", &n, &k);
    for(int i = 1; i < n; ++i) {
        scanf("%d%d%d", &x, &y, &c);
        G[x].push_back(pii(y, c));   
        G[y].push_back(pii(x, c));
    }
    dfs(1, 1, 0);
    printf("%.6lf\n", (double)cnt / n);
    return 0;
}

C

#include <stdio.h>
#include <math.h>
#include <string.h>
#include <algorithm>
using namespace std;
#define met(s) memset(s, 0, sizeof(s))
#define rep(i, a, b) for(int i = a; i <= b; ++i)
typedef long long LL;
typedef unsigned long long ull;
typedef pair<int, int> pii;
const int INF = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const int MAXN = 1e4 + 10;
int A[MAXN];
int a[MAXN], d[MAXN];
int dp[MAXN];
                 // 完全背包 dp[i]含义： 满足i的最小w 
                  
int main() {

	int n, m;
	scanf("%d %d", &n, &m);
	for(int i = 0; i < n; ++i) scanf("%d %d", &a[i], &d[i]);  //记录 v  w 
	dp[0] = 0;  //前0个花费0 
	for(int i = 1; i <= 10005; ++i) {
		dp[i] = INF;
		// i表示当前所需要的颜值
		for(int j = 0; j < m; ++j) {
			// 如果这个人对颜值的需求小于这匹马的需求，所花费的钱数变成dp[j]和d[i]中的较小者
			// ！！！这个if是关键
			if(i <= a[j]) dp[i] = min(d[j], dp[i]);
			// 完全背包
			else dp[i] = min(dp[i], dp[i - a[j]] + d[j]);
		}
	}
	for(int i = 0; i < m; ++i) {
		scanf("%d", &A[i]);
    	printf("%d%c", dp[A[i]], (i == m - 1) ? '\n' : ' ');
    }
    return 0;
}

E

时间复杂度是o（100*100/2） 直接暴力枚举

#include<bits/stdc++.h>
using namespace std;
int a[110];
int dp[110];
int main()
{
	int n,ans = 0;
	scanf("%d",&n);
	for (int i = 1;i <= n;i ++)
	{
		scanf("%d",&a[i]);
		ans = max(ans,a[i]);  //可以是其自身
	}
	for (int i = 1;i <= n;i ++)
	{
		int cnt = a[i];
		for (int j = i + 1;j <= n;j ++)
		{
			cnt = cnt ^ a[j];
			ans = max(ans,cnt);
		}
	}
	printf("%d\n",ans);		
	return 0;
}

I 

#include<bits/stdc++.h>
using namespace std;
int main()
{
	int t;
	scanf("%d",&t);
	while (t --)
	{
		int n,x,sum = 0;
		scanf("%d",&n);
		for (int i = 0;i < n;i ++)
		{
			scanf("%d",&x);
			sum += x;
		}
		printf("%d\n",(sum % n) ? n - 1 : n);
		printf("%d\n",min(n - sum % n,sum % n));
	}
	return 0;
}
// 无论怎么变化，和都是sum，若最后能够变成相等的数，则都为sum/n。
//若是无法变成都相等的 则最多变n-1个数相等 第n个数为 sum%n 比较下就好

#include<bits/stdc++.h>
using namespace std;
char maze[110][110];
int main()
{
	int n;
	while (~scanf("%d",&n))
	{
		int p = n,r = 1;
		memset(maze,' ',sizeof(maze));
		while (n >= 1)
		{
			for (int i = r;i <= n;i ++)
			{
				maze[r][i] = '*';
				maze[n][i] = '*';
				maze[i][r] = '*';
				maze[i][n] = '*';
			}                            //长度为n的方框的打印
			n -= 2;
			r += 2;           //依次减2 向内圈移动
		}
		for (int i = 1;i <= p;i ++)
		{
			for (int j = 1;j <= p;j ++)
				printf("%c",maze[i][j]);
			putchar('\n');
		}
	}
	return 0;
}